×

Fixed points and stability in neutral differential equations with variable delays. (English) Zbl 1136.34059

This paper deals with the asymptotic stability of a scalar neutral delay differential equation by means of the contraction mapping theorem, not the Lyapunov direct method. Some examples are included to illustrate the importance of the results.

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. A. Burton, Stability and periodic solutions of ordinary and functional-differential equations, Mathematics in Science and Engineering, vol. 178, Academic Press, Inc., Orlando, FL, 1985. · Zbl 0635.34001
[2] T. A. Burton, Liapunov functionals, fixed points, and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2002), no. 2, 181 – 190. · Zbl 1084.47522
[3] T. A. Burton, Stability by fixed point theory or Liapunov theory: a comparison, Fixed Point Theory 4 (2003), no. 1, 15 – 32. · Zbl 1061.47065
[4] T. A. Burton, Fixed points and stability of a nonconvolution equation, Proc. Amer. Math. Soc. 132 (2004), no. 12, 3679 – 3687. · Zbl 1050.34110
[5] T. A. Burton and Tetsuo Furumochi, A note on stability by Schauder’s theorem, Funkcial. Ekvac. 44 (2001), no. 1, 73 – 82. · Zbl 1158.34329
[6] T. A. Burton and Tetsuo Furumochi, Fixed points and problems in stability theory for ordinary and functional differential equations, Dynam. Systems Appl. 10 (2001), no. 1, 89 – 116. · Zbl 1021.34042
[7] T. A. Burton and Tetsuo Furumochi, Krasnoselskii’s fixed point theorem and stability, Nonlinear Anal. 49 (2002), no. 4, Ser. A: Theory Methods, 445 – 454. · Zbl 1015.34046
[8] Y. N. Raffoul, Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Math. Comput. Modelling 40 (2004), no. 7-8, 691 – 700. · Zbl 1083.34536
[9] B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Analysis, 63 (2005), e233-e242.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.